45
45

Sep 21, 2013
09/13

by
Paul A. Russell

texts

#
eye 45

#
favorite 0

#
comment 0

A family X of sets is said to be intersecting if any two members of X have non-empty intersection. It is a well-known and simple fact that an intersecting family of subsets of [n]={1,2,...,n} can contain at most 2^(n-1) sets. Katona, Katona and Katona ask the following question. Suppose instead a family X of subsets of [n] satisfies |X|=2^(n-1)+i for some fixed i>0. Create a new family X_p by choosing each member of X independently with some fixed probability p. How do we choose X to...

Source: http://arxiv.org/abs/1108.3207v1

38
38

Sep 23, 2013
09/13

by
Paul A. Russell

texts

#
eye 38

#
favorite 0

#
comment 0

We shall be interested in the following Erdos-Ko-Rado-type question. Fix some subset B of [n]. How large a family A of subsets of [n] can we find such that the intersection of any two sets in A contains a cyclic translate (modulo n) of B? Chung, Graham, Frankl and Shearer have proved that, in the case where B is a block of length t, we can do no better than to take A to consist of all supersets of B. We give an alternative proof of this result, which is in a certain sense more 'direct'.

Source: http://arxiv.org/abs/0710.1797v1

60
60

Sep 19, 2013
09/13

by
Paul A. Russell; Trevor J. Ponman; Alastair J. R. Sanderson

texts

#
eye 60

#
favorite 0

#
comment 0

We present an X-ray analysis of the radio-quiet cool-core galaxy group NGC 4325 (z=0.026) based on Chandra and ROSAT observations. The Chandra data were analysed using XSPEC deprojection, 2D spectral mapping and forward-fitting with parametric models. Additionally, a Markov chain Monte Carlo method was used to perform a joint Bayesian analysis of the Chandra and ROSAT data. The results of the various analysis methods are compared, particularly those obtained by forward-fitting and deprojection....

Source: http://arxiv.org/abs/astro-ph/0703010v1

37
37

Sep 23, 2013
09/13

by
Imre Leader; Paul A. Russell; Mark Walters

texts

#
eye 37

#
favorite 0

#
comment 0

A finite set $X$ in some Euclidean space $R^n$ is called Ramsey if for any $k$ there is a $d$ such that whenever $R^d$ is $k$-coloured it contains a monochromatic set congruent to $X$. This notion was introduced by Erdos, Graham, Montgomery, Rothschild, Spencer and Straus, who asked if a set is Ramsey if and only if it is spherical, meaning that it lies on the surface of a sphere. This question (made into a conjecture by Graham) has dominated subsequent work in Euclidean Ramsey theory. In this...

Source: http://arxiv.org/abs/1012.1350v1

57
57

Sep 21, 2013
09/13

by
Paul A. Russell; Mark Walters

texts

#
eye 57

#
favorite 0

#
comment 0

It is well known that an intersecting family of subsets of an n-element set can contain at most 2^(n-1) sets. It is natural to wonder how `close' to intersecting a family of size greater than 2^(n-1) can be. Katona, Katona and Katona introduced the idea of a `most probably intersecting family.' Suppose that X is a family and that 0

Source: http://arxiv.org/abs/1108.5603v1

51
51

Jul 20, 2013
07/13

by
Trevor A. Miles; Somak Raychaudhury; Paul A. Russell

texts

#
eye 51

#
favorite 0

#
comment 0

We present J and K-band luminosity functions (LF) for the Group Evolution Multiwavelength Study (GEMS) sample of 60 nearby groups of galaxies, with photometry from the 2MASS survey. We find that, as seen in B and R-band photometry of a subsample of these groups in our earlier work, the LFs of the X-ray dim groups (L_X < 10^41.7 erg/s) show a depletion of galaxies of intermediate luminosity around M_K = -23, within a radius 0.3R_500 from the centres of these groups. This feature is not seen...

Source: http://arxiv.org/abs/astro-ph/0609550v1

46
46

Sep 23, 2013
09/13

by
Imre Leader; Paul A. Russell; Mark Walters

texts

#
eye 46

#
favorite 0

#
comment 0

Motivated by some questions in Euclidean Ramsey theory, our aim in this note is to show that there exists a cyclic quadrilateral that does not embed into any transitive set (in any dimension). We show that in fact this holds for almost all cyclic quadrilaterals, and we also give explicit examples of such cyclic quadrilaterals. These are the first explicit examples of spherical sets that do not embed into transitive sets.

Source: http://arxiv.org/abs/1012.5468v1